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Jean Morlet Chair  | enregistrements trouvés : 119

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In these lectures, we will review what it means for a 3-manifold to have a hyperbolic structure, and give tools to show that a manifold is hyperbolic. We will also discuss how to decompose examples of 3-manifolds, such as knot complements, into simpler pieces. We give conditions that allow us to use these simpler pieces to determine information about the hyperbolic geometry of the original manifold. Most of the tools we present were developed in the 1970s, 80s, and 90s, but continue to have modern applications.
In these lectures, we will review what it means for a 3-manifold to have a hyperbolic structure, and give tools to show that a manifold is hyperbolic. We will also discuss how to decompose examples of 3-manifolds, such as knot complements, into simpler pieces. We give conditions that allow us to use these simpler pieces to determine information about the hyperbolic geometry of the original manifold. Most of the tools we present were developed in ...

57M27 ; 57M50 ; 57M25

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Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, then work of Kapovich-Kleiner proves the boundary of the group is homeomorphic to the Menger curve. However, their proof is very general and gives no tools to further study the boundary and large-scale geometry of these groups. In this talk, I will explain how to construct explicit embeddings of non-planar graphs into the boundary of these groups whenever the group is hyperbolic. Along the way, I will illustrate how our methods distinguish free-by-cyclic groups which are the fundamental group of a 3-manifold. This is joint work with Yael Algom-Kfir and Arnaud Hilion.
Given an automorphism of the free group, we consider the mapping torus defined with respect to the automorphism. If the automorphism is atoroidal, then the resulting free-by-cyclic group is hyperbolic by work of Brinkmann. In addition, if the automorphism is fully irreducible, then work of Kapovich-Kleiner proves the boundary of the group is homeomorphic to the Menger curve. However, their proof is very general and gives no tools to further ...

20F65 ; 20F67 ; 20E36

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Post-edited  Interview at Cirm: Shigeki Akiyama
Akiyama, Shigeki (Personne interviewée) | CIRM (Editeur )

Shigeki Akiyama is Professor at the Institute of Mathematics of the University of Tsukuba, Japan. A regular organizer of the annual workshop on quasi-periodic tilings at RIMS, he has also spent time as organizer or invited professor on several occasions in France (Paris, Marseille, Strasbourg) but also in Debrecen and at the Chinese University of Hong-Kong.
CIRM - Chaire Jean-Morlet 2017 - Aix-Marseille Université

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Bounded remainder sets for a dynamical system are sets for which the Birkhoff averages of return times differ from the expected values by at most a constant amount. These sets are rare and important objects which have been studied for over 100 years. In the last few years there have been a number of results which culminated in explicit constructions of bounded remainder sets for toral rotations in any dimension, of all possible allowable volumes. In this talk we are going to explain these results, and then explain how to generalize them to give explicit constructions of bounded remainder sets for rotations in $p$-adic solenoids. Our method of proof will make use of a natural dynamical encoding of patterns in non-Archimedean cut and project sets.
Bounded remainder sets for a dynamical system are sets for which the Birkhoff averages of return times differ from the expected values by at most a constant amount. These sets are rare and important objects which have been studied for over 100 years. In the last few years there have been a number of results which culminated in explicit constructions of bounded remainder sets for toral rotations in any dimension, of all possible allowable ...

11K06 ; 11K38 ; 11J71

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These lectures introduce the dynamical systems approach to tilings of Euclidean space, especially quasicrystalline tilings that have been constructed using a ‘supertile method’. Because tiling dynamics parallels one-dimensional symbolic dynamics, we discuss this case as well, highlighting the differences and similarities in the methods of study and the results that can be obtained.
In the first lecture we motivate the field with the discovery of quasicrystals, which led to D. Schectman’s winning the 2011 Nobel Prize in Chemistry. Then we set up the basics of tiling dynamics, describing tiling spaces, a tiling metric, and the shift or translation actions. Shift-invariant and ergodic measures are discussed, along with fundamental topological and dynamical properties.
The second lecture brings in the supertile construction methods, including symbolic substitutions, self-similar tilings, $S$-adic systems, and fusion rules. Numerous examples are given, most of which are not the “standard” examples, and we identify many commonalities and differences between these interrelated methods of construction. Then we compare and contrast dynamical results for supertile systems, highlighting those key insights that can be adapted to all cases.
In the third lecture we investigate one of the many current tiling research areas: spectral theory. Schectman made his Nobel-prize-winning discovery using diffraction analysis, and studying the mathematical version has been quite fruitful. Spectral theory of tiling dynamical systems is also of broad interest. We describe how these types of spectral analysis are carried out, give examples, and discuss what is known and unknown about the relationship between dynamical and diffraction analysis. Special attention is paid to the “point spectrum”, which is related to eigenfunctions and also to the bright spots that appear on diffraction images.
These lectures introduce the dynamical systems approach to tilings of Euclidean space, especially quasicrystalline tilings that have been constructed using a ‘supertile method’. Because tiling dynamics parallels one-dimensional symbolic dynamics, we discuss this case as well, highlighting the differences and similarities in the methods of study and the results that can be obtained.
In the first lecture we motivate the field with the discovery of ...

37B50 ; 37B10 ; 52C23

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Konstantin "Kostya" Mikhailovich Khanin is a Russian mathematician and physicist. Khanin received his PhD from the Landau Institute of Theoretical Physics in Moscow and continued working there as a research associate until 1994. Afterwards, he taught at Princeton University, at the Isaac Newton Institute in Cambridge, and at Heriot-Watt University before joining the faculty at the University of Toronto. Khanin was an invited speaker at the European Congress of Mathematics in Barcelona in 2000. He was a 2013 Simons Foundation Fellow. He held the Jean-Morlet Chair at the Centre International de Rencontres Mathématiques in 2017, and he is an Invited Speaker at the International Congress of Mathematicians in 2018 in Rio de Janeiro.
CIRM - Chaire Jean-Morlet 2017 - Aix-Marseille Université
Konstantin "Kostya" Mikhailovich Khanin is a Russian mathematician and physicist. Khanin received his PhD from the Landau Institute of Theoretical Physics in Moscow and continued working there as a research associate until 1994. Afterwards, he taught at Princeton University, at the Isaac Newton Institute in Cambridge, and at Heriot-Watt University before joining the faculty at the University of Toronto. Khanin was an invited speaker at the ...

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Post-edited  Interview at CIRM: Martin Hairer
Hairer, Martin (Personne interviewée) | CIRM (Editeur )

Martin Hairer KBE FRS (born 14 November 1975 in Geneva, Switzerland) is an Austrian mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. As of 2017 he is Regius Professor of Mathematics at the University of Warwick, having previously held a position at the Courant Institute of New York University. He was awarded the Fields Medal in 2014, one of the highest honours a mathematician can achieve.
Martin Hairer KBE FRS (born 14 November 1975 in Geneva, Switzerland) is an Austrian mathematician working in the field of stochastic analysis, in particular stochastic partial differential equations. As of 2017 he is Regius Professor of Mathematics at the University of Warwick, having previously held a position at the Courant Institute of New York University. He was awarded the Fields Medal in 2014, one of the highest honours a mathematician can ...

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Variational formulas for limit shapes of directed last-passage percolation models. Connections of minimizing cocycles of the variational formulas to geodesics, Busemann functions, and stationary percolation.

60K35 ; 60K37 ; 82C22 ; 82C43 ; 82D60

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Cubic surfaces in affine three space tend to have few integral points .However certain cubics such as $x^3 + y^3 + z^3 = m$, may have many such points but very little is known. We discuss these questions for Markoff type surfaces: $x^2 +y^2 +z^2 -x\cdot y\cdot z = m$ for which a (nonlinear) descent allows for a study. Specifically that of a Hasse Principle and strong approximation, together with "class numbers" and their averages for the corresponding nonlinear group of morphims of affine three space.
Cubic surfaces in affine three space tend to have few integral points .However certain cubics such as $x^3 + y^3 + z^3 = m$, may have many such points but very little is known. We discuss these questions for Markoff type surfaces: $x^2 +y^2 +z^2 -x\cdot y\cdot z = m$ for which a (nonlinear) descent allows for a study. Specifically that of a Hasse Principle and strong approximation, together with "class numbers" and their averages for the ...

11G05 ; 37A45

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Jean-Morlet Chair 2016 Semester 2 - CIRM Luminy.
Mariusz Lemanczyk (Nicolaus Copernicus University,Torun) and Sébastien Ferenczi (I2M - Aix-Marseille Université).
Semester on 'Ergodic Theory and Dynamical Systems in their Interactions with Arithmetic and Combinatorics'.
CIRM - Chaire Jean-Morlet 2016 - Aix-Marseille Université

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Post-edited  Interview at CIRM: Dipendra Prasad
Prasad, Dipendra (Personne interviewée) | CIRM (Editeur )

Jean-Morlet Chair 2016: Cirm is delighted to welcome Dipendra Prasad (Tata Institute of Fundamental Research in Mumbai) and Volker Heiermann (I2M Marseille) for six months.
Five scientific events are scheduled at CIRM between January and June 2016 and a range of worldwide guests will be invited over this period.
CIRM - Chaire Jean-Morlet 2016 - Aix-Marseille Université

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Beyond endoscopy is the strategy put forward by Langlands for applying the trace formula to the general principle of functoriality. Subsequent papers by Langlands (one in collaboration with Frenkel and Ngo), together with more recent papers by Altug, have refined the strategy. They all emphasize the importance of understanding the elliptic terms on the geometric side of the trace formula. We shall discuss the general strategy, and how it pertains to these terms.
Beyond endoscopy is the strategy put forward by Langlands for applying the trace formula to the general principle of functoriality. Subsequent papers by Langlands (one in collaboration with Frenkel and Ngo), together with more recent papers by Altug, have refined the strategy. They all emphasize the importance of understanding the elliptic terms on the geometric side of the trace formula. We shall discuss the general strategy, and how it ...

11F66 ; 22E50 ; 22E55

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Spherical Hecke algebra, Satake transform, and an introduction to local Langlands correspondence.
CIRM - Chaire Jean-Morlet 2016 - Aix-Marseille Université

20C08 ; 22E50 ; 11S37

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François Lalonde, Professor at the Mathematics and Statistics Department of the Université de Montréal, was named Director of the Centre de recherches mathématiques (CRM) on September 14, 2004. The CRM is the first institute of research in mathematical sciences founded in Canada in 1969.
A member of the Royal Society of Canada since 1997, François Lalonde's research is mainly in the field of Symplectic geometry and topology. From 1996 to 2000, he directed the Institut des sciences mathématiques (ISM), a consortium of six Québec universities (Montréal, McGill, UQAM, Concordia, Laval and Sherbrooke). In this capacity, he developed the Institute by putting in place measures furthering the place of Montréal, and Québec as a whole, as a North American centre of excellence in mathematical research and training.
Mr. Lalonde was also the Founder and Director of the Centre interuniversitaire de recherche en géométrie différentielle et en topologie (CIRGET) which gathers together the best geometers and topologists from UQAM, McGill, Montreal and Concordia universities.
A mathematician and physicist by training, François Lalonde holds a Doctorat d’Etat (1985) from Orsay Center in Paris, in the field of differential topology. He was a Killam Research Fellowship recipient in 2000-2002 and holds a Canada Research Chair in the field of Symplectic Geometry and Topology. He is member of the editorial committees of the Canadian Journal of Mathematics and of the Canadian Bulletin of Mathematics. Member of the scientific committee of the First Canada-France congress in 2004 and plenary speaker at the First Canada-China congress in 1999, his works in collaboration with Dusa McDuff were presented in her plenary address at the ICM in 1998. He is an invited speaker at the ICM 2006.
CIRM - Chaire Jean-Morlet 2015 - Aix-Marseille Université
François Lalonde, Professor at the Mathematics and Statistics Department of the Université de Montréal, was named Director of the Centre de recherches mathématiques (CRM) on September 14, 2004. The CRM is the first institute of research in mathematical sciences founded in Canada in 1969.
A member of the Royal Society of Canada since 1997, François Lalonde's research is mainly in the field of Symplectic geometry and topology. From 1996 to 2000, ...

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Theory of persistence modules is a rapidly developing field lying on the borderline between algebra, geometry and topology. It provides a very useful viewpoint at Morse theory, and at the same time is one of the cornerstones of topological data analysis. In the course I'll review foundations of this theory and focus on its applications to symplectic topology. In parts, the course is based on a recent work with Egor Shelukhin arXiv:1412.8277

37Cxx ; 37Jxx ; 53D25 ; 53D40 ; 53D42

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Post-edited  Interview at CIRM: Herwig Hauser
Hauser, Herwig (Personne interviewée) | CIRM (Editeur )

Herwig Hauser (Chair) and Guillaume Rond (Local Project Leader) held a Jean Morlet semester at CIRM from mid January to mid July 2015. Their scientific programme focused on 'Artin Approximation and Singularity Theory'. Artin Approximation concerns the solvability of algebraic equations in spaces of formal, convergent or algebraic power series. The classical version asserts that if a formal solution exists, then there also exists a convergent, hence analytic, and even algebraic solution which approximates the formal solution up to any given degree. As such, the theorem is instrumental for numerous constructions in algebraic geometry, commutative algebra and recursion theory in combinatorics. A series is Nash or algebraic if it is algebraic over the polynomials. Nash series can be codified by polynomial data deduced from the minimal polynomial by the normalization of the respective algebraic hypersurface. This makes them computable. The field has seen renewed activity through the recent research on Arc Spaces, Motivic Integration and Infinite Dimensional Geometry. Important questions remain still unanswered (nested subring case, composition problems, structure theorems for the solution sets) and were investigated during the program. Fruitful interchanges with the singularity theory, the combinatorics and the algebraic geometry groups took place. The scientific program was complemented by an exhibition of algebraic surfaces in the city of Marseille, based on the very successful "Imaginary" program designed by Hauser for the Mathematisches Forschungsinstitut Oberwolfach.
CIRM - Chaire Jean-Morlet 2015 - Aix-Marseille Université
Herwig Hauser (Chair) and Guillaume Rond (Local Project Leader) held a Jean Morlet semester at CIRM from mid January to mid July 2015. Their scientific programme focused on 'Artin Approximation and Singularity Theory'. Artin Approximation concerns the solvability of algebraic equations in spaces of formal, convergent or algebraic power series. The classical version asserts that if a formal solution exists, then there also exists a convergent, ...

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Post-edited  Interview at CIRM: Dusa McDuff
McDuff, Dusa (Personne interviewée) | CIRM (Editeur )

Dusa McDuff is the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College. At Barnard, she currently teaches "Calculus I", "Perspectives in Mathematics" and courses in geometry and topology.
Professor McDuff gained her early teaching experience at the University of York (U.K.), the University of Warwick (U.K.) and MIT. In 1978, she joined the faculty of the Department of Mathematics at SUNY Stony Brook, where she was awarded the title of Distinguished Professor in 1998.
Professor McDuff has honorary doctorates from the University of Edinburgh, the University of York, the University of Strasbourg and the University of St Andrews. She is a fellow of the Royal Society, a member of the National Academy of Sciences, a member of the American Philosophical Society, and an honorary fellow of Girton College, Cambridge.
She has received the Satter Prize from the American Mathematical Society and the Outstanding Woman Scientist Award from AWIS (Association for Women in Science).
Professor McDuff's service to the mathematical community has been extensive. She is particularly interested in issues connected with the position of women in mathematics, and currently serves on the MSRI Board of Trustees. Together with Dietmar Salamon, she has written several foundational books on symplectic topology as well as many research articles.
Dusa McDuff is the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College. At Barnard, she currently teaches "Calculus I", "Perspectives in Mathematics" and courses in geometry and topology.
Professor McDuff gained her early teaching experience at the University of York (U.K.), the University of Warwick (U.K.) and MIT. In 1978, she joined the faculty of the Department of Mathematics at SUNY Stony Brook, where she was awarded the ...

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I will discuss work in progress aimed towards defining contact homology using "virtual" holomorphic curve counting techniques.

37J10 ; 53D35 ; 53D40 ; 53D42 ; 53D45 ; 57R17

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Post-edited  Interview at CIRM: Michael Artin
Artin, Michael (Personne interviewée) | CIRM (Editeur )

Michael ARTIN participated in the "Artin Approximation and Infinite dimensional Geometry" event organized at CIRM in March 2015, which was part of the Jean-Morlet semester held by Herwig Hauser. Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry and also generally recognized as one of the outstanding professors in his field. Artin was born in Hamburg, Germany, and brought up in Indiana. His parents were Natalia Jasny (Natascha) and Emil Artin, a preeminent algebraist of the 20th century. In 2002, Artin won the American Mathematical Society's annual Steele Prize for Lifetime Achievement. In 2005, he was awarded the Harvard Centennial Medal. He won the Wolf Prize in Mathematics. He is also a member of the National Academy of Sciences and a Fellow of the American Academy of Arts and Sciences, the American Association for the Advancement of Science, the Society for Industrial and Applied Mathematics, and the American Mathematical Society.
Michael ARTIN participated in the "Artin Approximation and Infinite dimensional Geometry" event organized at CIRM in March 2015, which was part of the Jean-Morlet semester held by Herwig Hauser. Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry and also generally recognized as one of the outstanding professors ...

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